 In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.  Elements of Geometry - Page 24by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1837 - 376 pages
...same straight line, winch is impossible (Book I. Prop. XV. C«r. 2.). PROPOSITION IV. THEOREM. In ihe same circle, or in equal circles, equal arcs are subtended...; and, conversely, equal chords subtend equal arcs Note. When reference is made from one proposition to another, in th» Mine Book, the number of the... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...; for it has for its measure the half of an arc greater than a semicircumference. 111. Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Demonstration. Let the arc AB (fig. 52) be equal to ihe arc BC. ' Join AC; and, in the triangle ABC,... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...lines drawn from a given point to the same straight line, which is impossible (54). GEOM. 4 THEOREM. 102. In the same circle, or in equal circles, equal arcs are sub tended by equal chords, and, conversely, equal chords subtend equal arcs. pi6-«> Demonstration.... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...which is impossible. (Prop. 15. 1. Cor. 2.) Hence, A straight line, $c. PROPOSITION IV. THEOREM. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. If the radii AC, EO Dx-TP-v ^ are equal, and the arcs jj/ AMD, ENG; then the A chord AD will be equal... | |
 | Nathan Scholfield - 1845 - 894 pages
...the same right line, which is impossible, (Prop. XVII. Cor. 2. B. II.) PROPOSITION IV. THEOREM. In the same circle or in equal circles, equal arcs are...; and conversely equal chords subtend equal arcs. If the radii AC, EO, are equal, and the arcs AMD, ENG; then the chord AD will be equal to the chord... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...; for it has for its measure the half of an arc greater than a semicircumference. 112. Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Proof. Let the arc AB (fig. 52) be equal to the arc BC. Join AC ; and, in the triangle ABC, the angles... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...the same straight line, wmch is impossible (Book I. Prop. XV. Cor. 2.). PROPOSITION IV. THEOREM. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. Note. When reference is made from one proposition to another, in the same Book, the number of the proposition... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...impossible (Prop. XVII., Cor. 2, Book I.). Therefore, a straight line, &c. PROPOSITION III. THEOREM. In equal circles, equal arcs are subtended by equal...and, conversely, equal chords subtend equal arcs. Let ADB, EHF be equal circles, and let the arcs AID, EMH also be equal; then will the chord AD be equal... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...same straight line, which is impossible (B. L, P. 15, c. 2). GEOMETKY. PROPOSITION IV. THEOEEM. In the same circle, or in equal circles, equal arcs are...: and conversely, equal chords subtend equal arcs. Let 0 and 0 be the centres of two equal circles, and suppose the arc AMD equal to the arc ENG : then... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...1n a d1fferent Book, the number of the Book 1s also g1ven. 60 GEOMETRY. PROPOSITION IV. THEOREH. In the same circle, or in equal circles, equal arcs are...: and conversely, equal chords subtend equal arcs. Let C and O be the centres of two equal circles, and suppose the arc AMD equal to the arc ENG : then... | |
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